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This paper presents a complete mathematical model of a micro-grid set up with PV arrays. The model consists of mathematical design and development of PV module and arrays, power conditioning DC/DC converter and the inverter set up. These designs are integrated with an inverter controller that controls the voltage at a power system bus. The complete system is used as a micro-grid set up connected to a power grid. Testing and evaluations of the micro-grid is then conducted using off-grid and on-grid studies. The uniqueness of the proposed modeling and control includes a complete model's details of micro-grid set up with PV system, power conditioning devices and load model, the utilization of an MPPT and feedback controller to control the output voltage and current. Thus it provides an appropriate real-life testing platform for micro-grid connections to power grid. Simulation results show the effectiveness and the accuracy of this micro-grid model to emulate real-life scenarios.